(a) Define what it means for a context-free grammar (CFG) to be in Chomsky normal form (CNF). Give an example, with justification, of a context-free language (CFL) which is not defined by any CFG in CNF.

(b) Show that the intersection of two CFLs need not be a CFL.

(c) Let $L$ be a CFL over an alphabet $\Sigma$. Show that $\Sigma^{*} \backslash L$ need not be a CFL.